Thing is, doing proper pixel art (Think Bitmap brothers quality) is very time consuming and unless you are doing this full time you are going to cut some corners.
Gfx guys these days use Photoshop, paint in 24bit then do the palette conversion (down to 8bit or less) as a last step. It makes sense time wise, but you lose a lot of control over your palette and it almost never looks good.
Back in the day when I did pixel graphics, a lot of the time spent was to get a properly optimized palette. "Every color swatch motivated, no colors wasted" -mentality..

Well, you either do pixel art or you don't (I mean there's no need to cut corners). Usually painting in 24bit and then "downsampling" is guaranteed to provide you with a sub-par result (as you also mention) that would require much more work to get it into an acceptable (and usable) state than doing it the right way from the get go. This of course granted you'd like your result to really look and feel like pixel art (and not photorealistic or 3d rendered like).

That aside, you can still use Photoshop as a proper pixel art tool (as I do) by carefully selecting your palette and then drawing pixel by pixel, without using transparency/alpha at all (pencil tool, use clear cut fills with no anti-aliasing, nearest neighbor for resizes e.t.c.). I.e. the same way you'd do it on a classic Amiga paint program.